Question

If alpha and beta are the roots of equation x² + px + q find the value of alpha³beta + alphabeta³

Answer 1

Answer:

Explanation:

From xn+1+(x+1)n=0 we have

2xn+(n−1)xn−1+⋯+2=0 and also

xn+n−12xn−1+⋯+1=0. This polynomial obeys

(αβ)n1(βα)n2=1 with

n1 and n2 integers such that n1+n2=n

Calling now y=(αβ) we have

yn1−n2=y2n1−n=1→2n1−n=0→n=2r1

so n is an even integer.

Note.

α≠β because x=±1 is not root for

x2n+1+(x+1)2n=0

Answer by Raghav